when I update an app’s source file, I notice an alert automatically pops up on all the devices prompting to update. Is there any way to disable that, so that I can completely control which devices get the update

Instead of editing the app and uploading the new source file, why not create a new app with the updated source file? Go to Admin -> App Settings -> + Add New and add the new source file. Provide a different name for the app. As long as you push it to the device via policies (or directly), no devices will prompt to update the app.